“Slave Boy” « Search Results

Tuesday, December 5, 2017

Scully on Architecture

Filed under: General — m759 @ 10:18 pm

"It is not easy to set aside firmly seated preconceptions
in order to look at old material with fresh eyes —
hardest of all to face facts which, if true, are
so obvious and simple that they should patently have been
recognized long before."

— Vincent Scully, preface to the 1969 edition of
The Earth, the Temple, and the Gods: Greek Sacred Architecture

Monday, February 27, 2017

Logic for Jews

Filed under: General — Tags: Gopnik, Logic for Jews — m759 @ 9:07 pm

(Continued)

Adam Gopnik in The New Yorker today reacts to the startling
outcomes of three recent contests: the presidential election,
the Super Bowl, and the Oscar for Best Picture —

"The implicit dread logic is plain."

Related material —

Transformers in this journal and …

“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”

—Many Dimensions (1931), by Charles Williams

See also …

The above figure is from Ian Stewart's 1996 revision of a 1941 classic,
What Is Mathematics? , by Richard Courant and Herbert Robbins.

One wonders how the confused slave boy of Plato's Meno would react
to Stewart's remark that

"The number of copies required to double an
object's size depends on its dimension."

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Tuesday, September 27, 2016

Chomsky and Lévi-Strauss in China

Filed under: General,Geometry — Tags: Clash of the Titans, Mythspace, The Unity — m759 @ 7:31 am

Or: Philosophy for Jews

From a New Yorker weblog post dated Dec. 6, 2012 —

"Happy Birthday, Noam Chomsky" by Gary Marcus—

"… two titans facing off, with Chomsky, as ever,
defining the contest"

"Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew."

Socrates and the slave boy discussed a rather elementary "truth
about geometry" — A diamond inscribed in a square has area 2
(and side the square root of 2) if the square itself has area 4
(and side 2).

Consider that not-particularly-deep structure from the Meno dialogue
in the light of the following…

The following analysis of the Meno diagram from yesterday's
post "The Embedding" contradicts the Lévi-Strauss dictum on
the impossibility of going beyond a simple binary opposition.
(The Chinese word taiji denotes the fundamental concept in
Chinese philosophy that such a going-beyond is both useful
and possible.)

The matrix at left below represents the feminine yin principle
and the diamond at right represents the masculine yang .

The Embedding of Plato's Diamond in the Matrix

From a post of Sept. 22,
"Binary Opposition Illustrated" —

A symbol of the unity of yin and yang —

Related material:

A much more sophisticated approach to the "deep structure" of the
Meno diagram —

The larger cases —

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Monday, November 11, 2013

Steiner’s Modal Logic

Filed under: General — m759 @ 3:17 am

The first two pages of a 1989 book by George Steiner—

(Click to enlarge)

See also yesterday's posts The Field of the Possible
and Abstraction.

Compare and contrast with Socrates in the Meno
quoting Pindar then discussing with a slave boy
the duplication of the square.

Was Socrates a great philosopher or, as the above
figure seems to indicate and as some say of Steiner,
too clever by half ?

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Saturday, December 8, 2012

Defining the Contest…

Filed under: General,Geometry — Tags: Fitch, Geometry, Harvard Miller, on121208, Truchet Tiles, Wechsler Patterns — m759 @ 5:48 am

… Chomsky vs. Santa

From a New Yorker weblog yesterday—

"Happy Birthday, Noam Chomsky." by Gary Marcus—

"… two titans facing off, with Chomsky, as ever,
defining the contest"

See Meno Diamond in this journal. For instance, from
the Feast of Saint Nicholas (Dec. 6th) this year—

The Meno Embedding

Plato's Diamond embedded in The Matrix

For related truths about geometry, see the diamond theorem.

For a related contest of language theory vs. geometry,
see pattern theory (Sept. 11, 16, and 17, 2012).

See esp. the Sept. 11 post, on a Royal Society paper from July 2012
claiming that

"With the results presented here, we have taken the first steps
in decoding the uniquely human fascination with visual patterns,
what Gombrich* termed our ‘sense of order.’ "

The sorts of patterns discussed in the 2012 paper —

IMAGE- Diamond Theory patterns found in a 2012 Royal Society paper

"First steps"? The mathematics underlying such patterns
was presented 35 years earlier, in Diamond Theory.

* See Gombrich-Douat in this journal.

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Wednesday, September 19, 2012

Art Wars (continued)

Filed under: General,Geometry — m759 @ 8:00 pm

Today's previous post, "For Odin's Day," discussed
a mathematical object, the tesseract, from a strictly
narrative point of view.

In honor of George Balanchine, Odin might yield the
floor this evening to Apollo.

From a piece in today's online New York Times titled
"How a God Finds Art (the Abridged Version)"—

"… the newness at the heart of this story,
in which art is happening for the first time…."

Some related art—

and, more recently—

This more recent figure is from Ian Stewart's 1996 revision
of a 1941 classic, What Is Mathematics? , by Richard Courant
and Herbert Robbins.

Apollo might discuss with Socrates how the confused slave boy
of Plato's Meno would react to Stewart's remark that

"The number of copies required to double an
object's size depends on its dimension."

Apollo might also note an application of Socrates' Meno diagram
to the tesseract of this afternoon's Odin post—

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Wednesday, October 8, 2008

Wednesday October 8, 2008

Filed under: General,Geometry — Tags: Fields — m759 @ 12:00 pm

Serious Numbers

A Yom Kippur
Meditation

"When times are mysterious
Serious numbers
Will always be heard."
— Paul Simon,
"When Numbers Get Serious"

"There is a pleasantly discursive treatment of Pontius Pilate's unanswered question 'What is truth?'"

— H. S. M. Coxeter, introduction to Richard J. Trudeau's remarks on the "story theory" of truth as opposed to the "diamond theory" of truth in The Non-Euclidean Revolution

Trudeau's 1987 book uses the phrase "diamond theory" to denote the philosophical theory, common since Plato and Euclid, that there exist truths (which Trudeau calls "diamonds") that are certain and eternal– for instance, the truth in Euclidean geometry that the sum of a triangle's angles is 180 degrees. As the excerpt below shows, Trudeau prefers what he calls the "story theory" of truth–

"There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.'"

(By the way, the phrase "diamond theory" was used earlier, in 1976, as the title of a monograph on geometry of which Coxeter was aware.)

Richard J. Trudeau on the 'Story Theory' of truth

Excerpt from
The Non-Euclidean Revolution

What does this have to do with numbers?

Pilate's skeptical tone suggests he may have shared a certain confusion about geometric truth with thinkers like Trudeau and the slave boy in Plato's Meno. Truth in a different part of mathematics– elementary arithmetic– is perhaps more easily understood, although even there, the existence of what might be called "non-Euclidean number theory"– i.e., arithmetic over finite fields, in which 1+1 can equal zero– might prove baffling to thinkers like Trudeau.

Trudeau's book exhibits, though it does not discuss, a less confusing use of numbers– to mark the location of pages. For some philosophical background on this version of numerical truth that may be of interest to devotees of the Semitic religions on this evening's High Holiday, see Zen and Language Games.

For uses of numbers that are more confusing, see– for instance– the new website The Daily Beast and the old website Story Theory and the Number of the Beast.

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